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Solution of convection-diffusion model in groundwater pollution
Jalil Rashidinia1, Arefeh Momeni2, Mahboubeh Molavi-Arabshahi2
1Iran University of Science and Technology, School of Mathematics and Computer Science, Tehran, 16846-13114, Iran. rashidinia@iust.ac.ir.
Scientific Reports
|January 24, 2024
Summary
This study introduces an efficient spectral collocation method using orthogonalized Bernoulli polynomials to solve groundwater pollution problems. The novel approach offers computational savings and fast convergence for time-fractional convection-diffusion models.
Area of Science:
- Numerical analysis
- Environmental engineering
- Applied mathematics
Background:
- Groundwater pollution is a significant environmental concern.
- Time-fractional convection-diffusion equations model complex contaminant transport.
- Existing numerical methods can be computationally intensive.
Purpose of the Study:
- To develop a spectral collocation method for solving time-fractional convection-diffusion equations.
- To create operational matrices for fractional and classical derivatives using orthogonalized Bernoulli polynomials.
- To enhance computational efficiency and accuracy in groundwater pollution modeling.
Main Methods:
- Development of orthogonalized Bernoulli polynomials.
- Construction of sparse operational matrices for derivatives.
- Application of the spectral collocation method to time-fractional convection-diffusion problems.
Main Results:
- Achieved sparse operational matrices with unique non-zero entries.
- Demonstrated low computational cost and fast convergence.
- Validated the method's effectiveness and accuracy through two test problems.
Conclusions:
- The proposed spectral collocation method is accurate and efficient for groundwater pollution modeling.
- Orthogonalization of Bernoulli polynomials leads to computational advantages.
- The method shows superior performance compared to existing techniques.
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